Question

22 mark for review
f(x) = 9(4)^x
the function f is defined by the given equation. if g(x) = f(x + 2), which of the following equations defines the function g?
a g(x) = 18(4)^x
b g(x) = 144(4)^x
c g(x) = 18(8)^x
d g(x) = 81(16)^x

Explanation:

Step1: Substitute \( x + 2 \) into \( f(x) \)

Given \( f(x)=9(4)^{x} \), so \( g(x)=f(x + 2)=9(4)^{x + 2} \).

Step2: Apply exponent rule \( a^{m + n}=a^{m}\cdot a^{n} \)

Using the rule \( 4^{x + 2}=4^{x}\cdot4^{2} \), and \( 4^{2}=16 \), so \( g(x)=9\times16\times(4)^{x} \).

Step3: Calculate \( 9\times16 \)

\( 9\times16 = 144 \), so \( g(x)=144(4)^{x} \).

Answer:

B. \( g(x) = 144(4)^{x} \)